A 500.0 g metal block absorbs 1.125 × 104 J of heat to raise its temperature by 50.0 K. What is the substance?
Specific Heats of Selected Substances
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Substance C [J/(kg•K)]
Water (ice-)2,060
Iron-450
Aluminum-897
Gold- 130
Copper- 385
Silver- 235
Ammonia (liquid)-4,700
Water (liquid)- 4,180
Water (steam)- 2,020
Lead- 128
To determine the substance, we can use the formula:
Q = mcΔT
Where:
Q = heat absorbed or released
m = mass of the substance
c = specific heat of the substance
ΔT = change in temperature
Given:
Q = 1.125 × 10^4 J
m = 500.0 g
ΔT = 50.0 K
Rearranging the formula to solve for c:
c = Q / (mΔT)
Substituting the given values:
c = (1.125 × 10^4 J) / (500.0 g × 50.0 K)
Calculating:
c ≈ 0.45 J/(g•K)
Comparing this value to the specific heats of selected substances, we find that it matches the specific heat of iron, which is 450 J/(kg•K).
Therefore, the substance is iron.
To determine the substance, we need to calculate the specific heat capacity (C) of the material using the given values and compare it with the specific heat capacities listed for various substances.
The formula to calculate the specific heat capacity can be written as:
Q = m * C * ΔT
Where:
Q = heat absorbed (1.125 × 104 J)
m = mass of the metal block (500.0 g)
C = specific heat capacity
ΔT = change in temperature (50.0 K)
Rearranging the formula, we get:
C = Q / (m * ΔT)
Plugging in the values, we have:
C = (1.125 × 104 J) / (500.0 g * 50.0 K)
Simplifying the equation:
C = 2.25 J/(g•K)
Now, compare this specific heat capacity (C) with the values given in the table to find the matching substance. In this case, the specific heat capacity of 2.25 J/(g•K) matches with the specific heat capacity of aluminum, which is 897 J/(kg•K).
Therefore, the substance is aluminum.